Understanding Inflation-Indexed Bond Markets pot

79

JOHN Y. CAMPBELL

Harvard University

ROBERT J. SHILLER

Yale University

LUIS M. VICEIRA

Harvard University

Understanding Inflation-Indexed

Bond Markets

ABSTRACT This paper explores the history of inflation-indexed bond mar￾kets in the United States and the United Kingdom. It documents a massive

decline in long-term real interest rates from the 1990s until 2008, followed by

a sudden spike during the financial crisis of 2008. Breakeven inflation rates,

calculated from inflation-indexed and nominal government bond yields, were

stable from 2003 until the fall of 2008, when they showed dramatic declines.

The paper asks to what extent short-term real interest rates, bond risks, and

liquidity explain the trends before 2008 and the unusual developments that

followed. Low yields and high short-term volatility of returns do not invalidate

the basic case for inflation-indexed bonds, which is that they provide a safe

asset for long-term investors. Governments should expect inflation-indexed

bonds to be a relatively cheap form of debt financing in the future, even though

they have offered high returns over the past decade.

I

n recent years government-issued inflation-indexed bonds have become

available in a number of countries and have provided a fundamentally

new instrument for use in retirement saving. Because expected inflation

varies over time, conventional, nonindexed (nominal) Treasury bonds are

not safe in real terms; and because short-term real interest rates vary over

time, Treasury bills are not safe assets for long-term investors. Inflation￾indexed bonds fill this gap by offering a truly riskless long-term investment

(Campbell and Shiller 1997; Campbell and Viceira 2001, 2002; Brennan

and Xia 2002; Campbell, Chan, and Viceira 2003; Wachter 2003).

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The U.K. government first issued inflation-indexed bonds in the early

1980s, and the U.S. government followed suit by introducing Treasury

inflation-protected securities (TIPS) in 1997. Inflation-indexed government

bonds are also available in many other countries, including Canada, France,

and Japan. These bonds are now widely accepted financial instruments.

However, their history creates some new puzzles that deserve investigation.

First, given that the real interest rate is determined in the long run by

the marginal product of capital, one might expect inflation-indexed bond

yields to be extremely stable over time. But whereas 10-year annual yields

on U.K. inflation-indexed bonds averaged about 3.5 percent during the 1990s

(Barr and Campbell 1997), and those on U.S. TIPS exceeded 4 percent

around the turn of the millennium, by the mid-2000s yields on both coun￾tries’ bonds averaged below 2 percent, bottoming out at around 1 percent

in early 2008 before spiking to near 3 percent in late 2008. The massive

decline in long-term real interest rates from the 1990s to the 2000s is one

puzzle, and the instability in 2008 is another.

Second, in recent years inflation-indexed bond prices have tended to

move opposite to stock prices, so that these bonds have a negative “beta”

with the stock market and can be used to hedge equity risk. This has

been even more true of prices on nominal government bonds, although

these bonds behaved very differently in the 1970s and 1980s (Campbell,

Sunderam, and Viceira 2009). The reason for the negative beta on inflation￾indexed bonds is not well understood.

Third, given integrated world capital markets, one might expect that

inflation-indexed bond yields would be similar around the world. But this

is not always the case. During the first half of 2000, the yield gap between

U.S. and U.K. inflation-indexed bonds was over 2 percentage points,

although yields have since converged. In January 2008, 10-year yields

were similar in the United States and the United Kingdom, but elsewhere

yields ranged from 1.1 percent in Japan to almost 2.0 percent in France

(according to Bloomberg data). Yield differentials were even larger at

long maturities, with U.K. yields well below 1 percent and French yields

well above 2 percent.

To understand these phenomena, it is useful to distinguish three major

influences on inflation-indexed bond yields: current and expected future

short-term real interest rates; differences in expected returns on long-term

and short-term inflation-indexed bonds caused by risk premiums (which

can be negative if these bonds are valuable hedges); and differences in

expected returns on long-term and short-term bonds caused by liquidity

premiums or technical factors that segment the bond markets. The expecta￾80 Brookings Papers on Economic Activity, Spring 2009

11641-02a_Campbell_rev.qxd 8/14/09 12:48 PM Page 80

tions hypothesis of the term structure, applied to real interest rates, states

that only the first influence is time-varying whereas the other two are con￾stant. However, there is considerable evidence against this hypothesis for

nominal Treasury bonds, so it is important to allow for the possibility that

risk and liquidity premiums are time-varying.

The path of real interest rates is undoubtedly a major influence on

inflation-indexed bond yields. Indeed, before TIPS were issued, Campbell

and Shiller (1997) argued that one could anticipate how their yields would

behave by applying the expectations hypothesis of the term structure to real

interest rates. A first goal of this paper is to compare the history of inflation￾indexed bond yields with the implications of the expectations hypothesis,

and to explain how shocks to short-term real interest rates are transmitted

along the real yield curve.

Risk premiums on inflation-indexed bonds can be analyzed by applying

theoretical models of risk and return. Two leading paradigms deliver use￾ful insights. The consumption-based paradigm implies that risk premiums

on inflation-indexed bonds over short-term debt are negative if returns on

these bonds covary negatively with consumption, which will be the case if

consumption growth rates are persistent (Backus and Zin 1994; Campbell

1986; Gollier 2007; Piazzesi and Schneider 2007; Wachter 2006). The

capital asset pricing model (CAPM) implies that risk premiums on inflation￾indexed bonds will be negative if their prices covary negatively with stock

prices. The second paradigm has the advantage that it is easy to track the

covariance of inflation-indexed bonds and stocks using high-frequency data

on their prices, in the manner of Viceira and Mitsui (2007) and Campbell,

Adi Sunderam, and Viceira (2009).

Finally, it is important to take seriously the effects of institutional factors

on inflation-indexed bond yields. Plausibly, the high TIPS yields in the first

few years after their introduction were due to the slow development of TIPS

mutual funds and other indirect investment vehicles. Currently, long-term

inflation-indexed yields in the United Kingdom may be depressed by strong

demand from U.K. pension funds. The volatility of TIPS yields in the fall

of 2008 appears to have resulted in part from the unwinding of large insti￾tutional positions after the failure of the investment bank Lehman Brothers

in September. These institutional influences on yields can alternatively be

described as liquidity, market segmentation, or demand and supply effects

(Greenwood and Vayanos 2008).

This paper is organized as follows. Section I presents a graphical his￾tory of the inflation-indexed bond markets in the United States and the

United Kingdom, discussing bond supplies, the levels of yields, and the

JOHN Y. CAMPBELL, ROBERT J. SHILLER, and LUIS M. VICEIRA 81

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volatility and covariances with stocks of high-frequency movements in

yields. Section II asks what portion of the TIPS yield history can be

explained by movements in short-term real interest rates, together with

the expectations hypothesis of the term structure. This section revisits

the vector autoregression (VAR) analysis of Campbell and Shiller (1997).

Section III discusses the risk characteristics of TIPS and estimates a model

of TIPS pricing with time-varying systematic risk, a variant of the model

in Campbell, Sunderam, and Viceira (2009), to see how much of the yield

history can be explained by changes in risk. Section IV discusses the unusual

market conditions that prevailed in the fall of 2008 and the channels through

which they might have influenced inflation-indexed bond yields. Sec￾tion V draws implications for investors and policymakers. An appendix

available online presents technical details of our bond pricing model and

of data construction.1

I. The History of Inflation-Indexed Bond Markets

The top panel of figure 1 shows the growth of the outstanding supply of

TIPS during the past 10 years. From modest beginnings in 1997, TIPS

grew to around 10 percent of the marketable debt of the U.S. Treasury, and

more than 3.5 percent of U.S. GDP, in 2008. This growth has been fairly

smooth, with a minor slowdown in 2001–02. The bottom panel shows a

comparable history for U.K. inflation-indexed gilts (government bonds).

From equally modest beginnings in 1982, the stock of these bonds has

grown rapidly and accounted for almost 30 percent of the British public

debt in 2008, equivalent to about 10 percent of GDP. Growth in the inflation￾indexed share of the public debt slowed in 1990–97 and reversed in 2004–05

but otherwise proceeded at a rapid rate.

The top panel of figure 2 plots yields on 10-year nominal and inflation￾indexed U.S. Treasury bonds from January 1998, a year after their intro￾duction, through March 2009.2 The figure shows a considerable decline in

both nominal and real long-term interest rates since TIPS yields peaked

early in 2000. Through 2007 the decline was roughly parallel, as inflation￾indexed bond yields fell from slightly over 4 percent to slightly over

82 Brookings Papers on Economic Activity, Spring 2009

1. The online appendix can be found at kuznets.fas.harvard.edu/∼campbell/papers.html.

2. We calculate the yield for the longest-maturity inflation-indexed bond outstanding at

each point in time whose original maturity at issue was 10 years. This is the on-the-run TIPS

issue. We obtain constant-maturity 10-year yields for nominal Treasury bonds from the Center

for Research in Security Prices (CRSP) database. Details of data construction are reported in

the online appendix.

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JOHN Y. CAMPBELL, ROBERT J. SHILLER, and LUIS M. VICEIRA 83

1 percent, while yields on nominal government bonds fell from around

7 percent to 4 percent. Thus, this was a period in which both nominal

and inflation-indexed Treasury bond yields were driven down by a large

decline in long-term real interest rates. In 2008, in contrast, nominal

Treasury yields continued to decline, while TIPS yields spiked above

3 percent toward the end of the year.

The bottom panel of figure 2 shows a comparable history for the United

Kingdom since the early 1990s. To facilitate comparison of the two plots,

the beginning of the U.S. sample period is marked with a vertical line. The

downward trend in inflation-indexed yields is even more dramatic over

this longer period. U.K. inflation-indexed gilts also experienced a dramatic

yield spike in the fall of 2008.

Figure 1. Stocks of Inflation-Indexed Government Bonds Outstanding

Percent

United States

Sources: Treasury Bulletin, various issues, table FD-2; Heriot-Watt/Faculty and Institute of Actuaries

Gilt Database (www.ma.hw.ac.uk/~andrewc/gilts/, file BGSAmounts.xls).

2

4

6

8

10

As percent of GDP

As share of all government debt

1998 2000 2002 2004 2006 2008

Percent

United Kingdom

As percent of GDP

As share of all government debt

5

10

15

20

25

1985 1990 1995 2000 2005

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The top panel of figure 3 plots the 10-year breakeven inflation rate, the

difference between 10-year nominal and inflation-indexed Treasury bond

yields. The breakeven inflation rate was fairly volatile in the first few years

of the TIPS market; it then stabilized between 1.5 and 2.0 percent a year in

the early years of this decade before creeping up to about 2.5 percent from

2004 through 2007. In 2008 the breakeven inflation rate collapsed, reaching

almost zero at the end of the year. The figure also shows, for the early years

of the sample, the subsequently realized 3-year inflation rate. After the first

84 Brookings Papers on Economic Activity, Spring 2009

Figure 2. Yields on Ten-Year Nominal and Inflation-Indexed Government Bonds,

1991–2009a

Percent a year

United States

Source: Authorsí calc ulations using data from Bloomberg and Heriot-Watt/Faculty and Institute of

Actuaries Gilt Database; see the online appendix (kuznets.fas.harvard.edu/~campbell/papers.html) for

details.

a. Yields are calculated from spliced yields and price data of individual issuances.

2

4

6

8

10

2

4

6

8

10

Percent a year

United Kingdom

Nominal

1992 1994 1996 1998 2000 2002 2004 2006 2008

1992 1994 1996 1998 2000 2002 2004 2006 2008

Inflation-indexed

Nominal

Inflation-indexed

TIPS introduced

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